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authorDan Albert <danalbert@google.com>2015-10-13 16:28:19 -0700
committerDan Albert <danalbert@google.com>2015-10-13 16:28:19 -0700
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Change-Id: Iee9c6985c613f58c82e33a91722d371579eb290f
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-------------------------------------------------------------------------------
--- --
--- GNAT RUN-TIME COMPONENTS --
--- --
--- S Y S T E M . R A N D O M _ N U M B E R S --
--- --
--- B o d y --
--- --
--- Copyright (C) 2007-2012, Free Software Foundation, Inc. --
--- --
--- GNAT is free software; you can redistribute it and/or modify it under --
--- terms of the GNU General Public License as published by the Free Soft- --
--- ware Foundation; either version 3, or (at your option) any later ver- --
--- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
--- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
--- or FITNESS FOR A PARTICULAR PURPOSE. --
--- --
--- As a special exception under Section 7 of GPL version 3, you are granted --
--- additional permissions described in the GCC Runtime Library Exception, --
--- version 3.1, as published by the Free Software Foundation. --
--- --
--- You should have received a copy of the GNU General Public License and --
--- a copy of the GCC Runtime Library Exception along with this program; --
--- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
--- <http://www.gnu.org/licenses/>. --
--- --
--- GNAT was originally developed by the GNAT team at New York University. --
--- Extensive contributions were provided by Ada Core Technologies Inc. --
--- --
-------------------------------------------------------------------------------
-
-------------------------------------------------------------------------------
--- --
--- The implementation here is derived from a C-program for MT19937, with --
--- initialization improved 2002/1/26. As required, the following notice is --
--- copied from the original program. --
--- --
--- Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura, --
--- All rights reserved. --
--- --
--- Redistribution and use in source and binary forms, with or without --
--- modification, are permitted provided that the following conditions --
--- are met: --
--- --
--- 1. Redistributions of source code must retain the above copyright --
--- notice, this list of conditions and the following disclaimer. --
--- --
--- 2. Redistributions in binary form must reproduce the above copyright --
--- notice, this list of conditions and the following disclaimer in the --
--- documentation and/or other materials provided with the distribution.--
--- --
--- 3. The names of its contributors may not be used to endorse or promote --
--- products derived from this software without specific prior written --
--- permission. --
--- --
--- THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS --
--- "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT --
--- LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR --
--- A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT --
--- OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, --
--- SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED --
--- TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR --
--- PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF --
--- LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING --
--- NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS --
--- SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. --
--- --
-------------------------------------------------------------------------------
-
-------------------------------------------------------------------------------
--- --
--- This is an implementation of the Mersenne Twister, twisted generalized --
--- feedback shift register of rational normal form, with state-bit --
--- reflection and tempering. This version generates 32-bit integers with a --
--- period of 2**19937 - 1 (a Mersenne prime, hence the name). For --
--- applications requiring more than 32 bits (up to 64), we concatenate two --
--- 32-bit numbers. --
--- --
--- See http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html for --
--- details. --
--- --
--- In contrast to the original code, we do not generate random numbers in --
--- batches of N. Measurement seems to show this has very little if any --
--- effect on performance, and it may be marginally better for real-time --
--- applications with hard deadlines. --
--- --
-------------------------------------------------------------------------------
-
-with Ada.Unchecked_Conversion;
-
-with System.Random_Seed;
-
-with Interfaces; use Interfaces;
-
-use Ada;
-
-package body System.Random_Numbers is
-
- Image_Numeral_Length : constant := Max_Image_Width / N;
- subtype Image_String is String (1 .. Max_Image_Width);
-
- ----------------------------
- -- Algorithmic Parameters --
- ----------------------------
-
- Lower_Mask : constant := 2**31-1;
- Upper_Mask : constant := 2**31;
-
- Matrix_A : constant array (State_Val range 0 .. 1) of State_Val
- := (0, 16#9908b0df#);
- -- The twist transformation is represented by a matrix of the form
- --
- -- [ 0 I(31) ]
- -- [ _a ]
- --
- -- where 0 is a 31x31 block of 0s, I(31) is the 31x31 identity matrix and
- -- _a is a particular bit row-vector, represented here by a 32-bit integer.
- -- If integer x represents a row vector of bits (with x(0), the units bit,
- -- last), then
- -- x * A = [0 x(31..1)] xor Matrix_A(x(0)).
-
- U : constant := 11;
- S : constant := 7;
- B_Mask : constant := 16#9d2c5680#;
- T : constant := 15;
- C_Mask : constant := 16#efc60000#;
- L : constant := 18;
- -- The tempering shifts and bit masks, in the order applied
-
- Seed0 : constant := 5489;
- -- Default seed, used to initialize the state vector when Reset not called
-
- Seed1 : constant := 19650218;
- -- Seed used to initialize the state vector when calling Reset with an
- -- initialization vector.
-
- Mult0 : constant := 1812433253;
- -- Multiplier for a modified linear congruential generator used to
- -- initialize the state vector when calling Reset with a single integer
- -- seed.
-
- Mult1 : constant := 1664525;
- Mult2 : constant := 1566083941;
- -- Multipliers for two modified linear congruential generators used to
- -- initialize the state vector when calling Reset with an initialization
- -- vector.
-
- -----------------------
- -- Local Subprograms --
- -----------------------
-
- procedure Init (Gen : Generator; Initiator : Unsigned_32);
- -- Perform a default initialization of the state of Gen. The resulting
- -- state is identical for identical values of Initiator.
-
- procedure Insert_Image
- (S : in out Image_String;
- Index : Integer;
- V : State_Val);
- -- Insert image of V into S, in the Index'th 11-character substring
-
- function Extract_Value (S : String; Index : Integer) return State_Val;
- -- Treat S as a sequence of 11-character decimal numerals and return
- -- the result of converting numeral #Index (numbering from 0)
-
- function To_Unsigned is
- new Unchecked_Conversion (Integer_32, Unsigned_32);
- function To_Unsigned is
- new Unchecked_Conversion (Integer_64, Unsigned_64);
-
- ------------
- -- Random --
- ------------
-
- function Random (Gen : Generator) return Unsigned_32 is
- G : Generator renames Gen.Writable.Self.all;
- Y : State_Val;
- I : Integer; -- should avoid use of identifier I ???
-
- begin
- I := G.I;
-
- if I < N - M then
- Y := (G.S (I) and Upper_Mask) or (G.S (I + 1) and Lower_Mask);
- Y := G.S (I + M) xor Shift_Right (Y, 1) xor Matrix_A (Y and 1);
- I := I + 1;
-
- elsif I < N - 1 then
- Y := (G.S (I) and Upper_Mask) or (G.S (I + 1) and Lower_Mask);
- Y := G.S (I + (M - N))
- xor Shift_Right (Y, 1)
- xor Matrix_A (Y and 1);
- I := I + 1;
-
- elsif I = N - 1 then
- Y := (G.S (I) and Upper_Mask) or (G.S (0) and Lower_Mask);
- Y := G.S (M - 1) xor Shift_Right (Y, 1) xor Matrix_A (Y and 1);
- I := 0;
-
- else
- Init (G, Seed0);
- return Random (Gen);
- end if;
-
- G.S (G.I) := Y;
- G.I := I;
-
- Y := Y xor Shift_Right (Y, U);
- Y := Y xor (Shift_Left (Y, S) and B_Mask);
- Y := Y xor (Shift_Left (Y, T) and C_Mask);
- Y := Y xor Shift_Right (Y, L);
-
- return Y;
- end Random;
-
- generic
- type Unsigned is mod <>;
- type Real is digits <>;
- with function Random (G : Generator) return Unsigned is <>;
- function Random_Float_Template (Gen : Generator) return Real;
- pragma Inline (Random_Float_Template);
- -- Template for a random-number generator implementation that delivers
- -- values of type Real in the range [0 .. 1], using values from Gen,
- -- assuming that Unsigned is large enough to hold the bits of a mantissa
- -- for type Real.
-
- ---------------------------
- -- Random_Float_Template --
- ---------------------------
-
- function Random_Float_Template (Gen : Generator) return Real is
-
- pragma Compile_Time_Error
- (Unsigned'Last <= 2**(Real'Machine_Mantissa - 1),
- "insufficiently large modular type used to hold mantissa");
-
- begin
- -- This code generates random floating-point numbers from unsigned
- -- integers. Assuming that Real'Machine_Radix = 2, it can deliver all
- -- machine values of type Real (as implied by Real'Machine_Mantissa and
- -- Real'Machine_Emin), which is not true of the standard method (to
- -- which we fall back for non-binary radix): computing Real(<random
- -- integer>) / (<max random integer>+1). To do so, we first extract an
- -- (M-1)-bit significand (where M is Real'Machine_Mantissa), and then
- -- decide on a normalized exponent by repeated coin flips, decrementing
- -- from 0 as long as we flip heads (1 bits). This process yields the
- -- proper geometric distribution for the exponent: in a uniformly
- -- distributed set of floating-point numbers, 1/2 of them will be in
- -- (0.5, 1], 1/4 will be in (0.25, 0.5], and so forth. It makes a
- -- further adjustment at binade boundaries (see comments below) to give
- -- the effect of selecting a uniformly distributed real deviate in
- -- [0..1] and then rounding to the nearest representable floating-point
- -- number. The algorithm attempts to be stingy with random integers. In
- -- the worst case, it can consume roughly -Real'Machine_Emin/32 32-bit
- -- integers, but this case occurs with probability around
- -- 2**Machine_Emin, and the expected number of calls to integer-valued
- -- Random is 1. For another discussion of the issues addressed by this
- -- process, see Allen Downey's unpublished paper at
- -- http://allendowney.com/research/rand/downey07randfloat.pdf.
-
- if Real'Machine_Radix /= 2 then
- return Real'Machine
- (Real (Unsigned'(Random (Gen))) * 2.0**(-Unsigned'Size));
-
- else
- declare
- type Bit_Count is range 0 .. 4;
-
- subtype T is Real'Base;
-
- Trailing_Ones : constant array (Unsigned_32 range 0 .. 15)
- of Bit_Count :=
- (2#00000# => 0, 2#00001# => 1, 2#00010# => 0, 2#00011# => 2,
- 2#00100# => 0, 2#00101# => 1, 2#00110# => 0, 2#00111# => 3,
- 2#01000# => 0, 2#01001# => 1, 2#01010# => 0, 2#01011# => 2,
- 2#01100# => 0, 2#01101# => 1, 2#01110# => 0, 2#01111# => 4);
-
- Pow_Tab : constant array (Bit_Count range 0 .. 3) of Real
- := (0 => 2.0**(0 - T'Machine_Mantissa),
- 1 => 2.0**(-1 - T'Machine_Mantissa),
- 2 => 2.0**(-2 - T'Machine_Mantissa),
- 3 => 2.0**(-3 - T'Machine_Mantissa));
-
- Extra_Bits : constant Natural :=
- (Unsigned'Size - T'Machine_Mantissa + 1);
- -- Random bits left over after selecting mantissa
-
- Mantissa : Unsigned;
-
- X : Real; -- Scaled mantissa
- R : Unsigned_32; -- Supply of random bits
- R_Bits : Natural; -- Number of bits left in R
- K : Bit_Count; -- Next decrement to exponent
-
- begin
- Mantissa := Random (Gen) / 2**Extra_Bits;
- R := Unsigned_32 (Mantissa mod 2**Extra_Bits);
- R_Bits := Extra_Bits;
- X := Real (2**(T'Machine_Mantissa - 1) + Mantissa); -- Exact
-
- if Extra_Bits < 4 and then R < 2 ** Extra_Bits - 1 then
-
- -- We got lucky and got a zero in our few extra bits
-
- K := Trailing_Ones (R);
-
- else
- Find_Zero : loop
-
- -- R has R_Bits unprocessed random bits, a multiple of 4.
- -- X needs to be halved for each trailing one bit. The
- -- process stops as soon as a 0 bit is found. If R_Bits
- -- becomes zero, reload R.
-
- -- Process 4 bits at a time for speed: the two iterations
- -- on average with three tests each was still too slow,
- -- probably because the branches are not predictable.
- -- This loop now will only execute once 94% of the cases,
- -- doing more bits at a time will not help.
-
- while R_Bits >= 4 loop
- K := Trailing_Ones (R mod 16);
-
- exit Find_Zero when K < 4; -- Exits 94% of the time
-
- R_Bits := R_Bits - 4;
- X := X / 16.0;
- R := R / 16;
- end loop;
-
- -- Do not allow us to loop endlessly even in the (very
- -- unlikely) case that Random (Gen) keeps yielding all ones.
-
- exit Find_Zero when X = 0.0;
- R := Random (Gen);
- R_Bits := 32;
- end loop Find_Zero;
- end if;
-
- -- K has the count of trailing ones not reflected yet in X. The
- -- following multiplication takes care of that, as well as the
- -- correction to move the radix point to the left of the mantissa.
- -- Doing it at the end avoids repeated rounding errors in the
- -- exceedingly unlikely case of ever having a subnormal result.
-
- X := X * Pow_Tab (K);
-
- -- The smallest value in each binade is rounded to by 0.75 of
- -- the span of real numbers as its next larger neighbor, and
- -- 1.0 is rounded to by half of the span of real numbers as its
- -- next smaller neighbor. To account for this, when we encounter
- -- the smallest number in a binade, we substitute the smallest
- -- value in the next larger binade with probability 1/2.
-
- if Mantissa = 0 and then Unsigned_32'(Random (Gen)) mod 2 = 0 then
- X := 2.0 * X;
- end if;
-
- return X;
- end;
- end if;
- end Random_Float_Template;
-
- ------------
- -- Random --
- ------------
-
- function Random (Gen : Generator) return Float is
- function F is new Random_Float_Template (Unsigned_32, Float);
- begin
- return F (Gen);
- end Random;
-
- function Random (Gen : Generator) return Long_Float is
- function F is new Random_Float_Template (Unsigned_64, Long_Float);
- begin
- return F (Gen);
- end Random;
-
- function Random (Gen : Generator) return Unsigned_64 is
- begin
- return Shift_Left (Unsigned_64 (Unsigned_32'(Random (Gen))), 32)
- or Unsigned_64 (Unsigned_32'(Random (Gen)));
- end Random;
-
- ---------------------
- -- Random_Discrete --
- ---------------------
-
- function Random_Discrete
- (Gen : Generator;
- Min : Result_Subtype := Default_Min;
- Max : Result_Subtype := Result_Subtype'Last) return Result_Subtype
- is
- begin
- if Max = Min then
- return Max;
-
- elsif Max < Min then
- raise Constraint_Error;
-
- elsif Result_Subtype'Base'Size > 32 then
- declare
- -- In the 64-bit case, we have to be careful, since not all 64-bit
- -- unsigned values are representable in GNAT's root_integer type.
- -- Ignore different-size warnings here since GNAT's handling
- -- is correct.
-
- pragma Warnings ("Z");
- function Conv_To_Unsigned is
- new Unchecked_Conversion (Result_Subtype'Base, Unsigned_64);
- function Conv_To_Result is
- new Unchecked_Conversion (Unsigned_64, Result_Subtype'Base);
- pragma Warnings ("z");
-
- N : constant Unsigned_64 :=
- Conv_To_Unsigned (Max) - Conv_To_Unsigned (Min) + 1;
-
- X, Slop : Unsigned_64;
-
- begin
- if N = 0 then
- return Conv_To_Result (Conv_To_Unsigned (Min) + Random (Gen));
-
- else
- Slop := Unsigned_64'Last rem N + 1;
-
- loop
- X := Random (Gen);
- exit when Slop = N or else X <= Unsigned_64'Last - Slop;
- end loop;
-
- return Conv_To_Result (Conv_To_Unsigned (Min) + X rem N);
- end if;
- end;
-
- elsif Result_Subtype'Pos (Max) - Result_Subtype'Pos (Min) =
- 2 ** 32 - 1
- then
- return Result_Subtype'Val
- (Result_Subtype'Pos (Min) + Unsigned_32'Pos (Random (Gen)));
- else
- declare
- N : constant Unsigned_32 :=
- Unsigned_32 (Result_Subtype'Pos (Max) -
- Result_Subtype'Pos (Min) + 1);
- Slop : constant Unsigned_32 := Unsigned_32'Last rem N + 1;
- X : Unsigned_32;
-
- begin
- loop
- X := Random (Gen);
- exit when Slop = N or else X <= Unsigned_32'Last - Slop;
- end loop;
-
- return
- Result_Subtype'Val
- (Result_Subtype'Pos (Min) + Unsigned_32'Pos (X rem N));
- end;
- end if;
- end Random_Discrete;
-
- ------------------
- -- Random_Float --
- ------------------
-
- function Random_Float (Gen : Generator) return Result_Subtype is
- begin
- if Result_Subtype'Base'Digits > Float'Digits then
- return Result_Subtype'Machine (Result_Subtype
- (Long_Float'(Random (Gen))));
- else
- return Result_Subtype'Machine (Result_Subtype
- (Float'(Random (Gen))));
- end if;
- end Random_Float;
-
- -----------
- -- Reset --
- -----------
-
- procedure Reset (Gen : Generator) is
- begin
- Init (Gen, Unsigned_32'Mod (Random_Seed.Get_Seed));
- end Reset;
-
- procedure Reset (Gen : Generator; Initiator : Integer_32) is
- begin
- Init (Gen, To_Unsigned (Initiator));
- end Reset;
-
- procedure Reset (Gen : Generator; Initiator : Unsigned_32) is
- begin
- Init (Gen, Initiator);
- end Reset;
-
- procedure Reset (Gen : Generator; Initiator : Integer) is
- begin
- -- This is probably an unnecessary precaution against future change, but
- -- since the test is a static expression, no extra code is involved.
-
- if Integer'Size <= 32 then
- Init (Gen, To_Unsigned (Integer_32 (Initiator)));
-
- else
- declare
- Initiator1 : constant Unsigned_64 :=
- To_Unsigned (Integer_64 (Initiator));
- Init0 : constant Unsigned_32 :=
- Unsigned_32 (Initiator1 mod 2 ** 32);
- Init1 : constant Unsigned_32 :=
- Unsigned_32 (Shift_Right (Initiator1, 32));
- begin
- Reset (Gen, Initialization_Vector'(Init0, Init1));
- end;
- end if;
- end Reset;
-
- procedure Reset (Gen : Generator; Initiator : Initialization_Vector) is
- G : Generator renames Gen.Writable.Self.all;
- I, J : Integer;
-
- begin
- Init (G, Seed1);
- I := 1;
- J := 0;
-
- if Initiator'Length > 0 then
- for K in reverse 1 .. Integer'Max (N, Initiator'Length) loop
- G.S (I) :=
- (G.S (I) xor ((G.S (I - 1)
- xor Shift_Right (G.S (I - 1), 30)) * Mult1))
- + Initiator (J + Initiator'First) + Unsigned_32 (J);
-
- I := I + 1;
- J := J + 1;
-
- if I >= N then
- G.S (0) := G.S (N - 1);
- I := 1;
- end if;
-
- if J >= Initiator'Length then
- J := 0;
- end if;
- end loop;
- end if;
-
- for K in reverse 1 .. N - 1 loop
- G.S (I) :=
- (G.S (I) xor ((G.S (I - 1)
- xor Shift_Right (G.S (I - 1), 30)) * Mult2))
- - Unsigned_32 (I);
- I := I + 1;
-
- if I >= N then
- G.S (0) := G.S (N - 1);
- I := 1;
- end if;
- end loop;
-
- G.S (0) := Upper_Mask;
- end Reset;
-
- procedure Reset (Gen : Generator; From_State : Generator) is
- G : Generator renames Gen.Writable.Self.all;
- begin
- G.S := From_State.S;
- G.I := From_State.I;
- end Reset;
-
- procedure Reset (Gen : Generator; From_State : State) is
- G : Generator renames Gen.Writable.Self.all;
- begin
- G.I := 0;
- G.S := From_State;
- end Reset;
-
- procedure Reset (Gen : Generator; From_Image : String) is
- G : Generator renames Gen.Writable.Self.all;
- begin
- G.I := 0;
-
- for J in 0 .. N - 1 loop
- G.S (J) := Extract_Value (From_Image, J);
- end loop;
- end Reset;
-
- ----------
- -- Save --
- ----------
-
- procedure Save (Gen : Generator; To_State : out State) is
- Gen2 : Generator;
-
- begin
- if Gen.I = N then
- Init (Gen2, 5489);
- To_State := Gen2.S;
-
- else
- To_State (0 .. N - 1 - Gen.I) := Gen.S (Gen.I .. N - 1);
- To_State (N - Gen.I .. N - 1) := Gen.S (0 .. Gen.I - 1);
- end if;
- end Save;
-
- -----------
- -- Image --
- -----------
-
- function Image (Of_State : State) return String is
- Result : Image_String;
-
- begin
- Result := (others => ' ');
-
- for J in Of_State'Range loop
- Insert_Image (Result, J, Of_State (J));
- end loop;
-
- return Result;
- end Image;
-
- function Image (Gen : Generator) return String is
- Result : Image_String;
-
- begin
- Result := (others => ' ');
- for J in 0 .. N - 1 loop
- Insert_Image (Result, J, Gen.S ((J + Gen.I) mod N));
- end loop;
-
- return Result;
- end Image;
-
- -----------
- -- Value --
- -----------
-
- function Value (Coded_State : String) return State is
- Gen : Generator;
- S : State;
- begin
- Reset (Gen, Coded_State);
- Save (Gen, S);
- return S;
- end Value;
-
- ----------
- -- Init --
- ----------
-
- procedure Init (Gen : Generator; Initiator : Unsigned_32) is
- G : Generator renames Gen.Writable.Self.all;
- begin
- G.S (0) := Initiator;
-
- for I in 1 .. N - 1 loop
- G.S (I) :=
- (G.S (I - 1) xor Shift_Right (G.S (I - 1), 30)) * Mult0
- + Unsigned_32 (I);
- end loop;
-
- G.I := 0;
- end Init;
-
- ------------------
- -- Insert_Image --
- ------------------
-
- procedure Insert_Image
- (S : in out Image_String;
- Index : Integer;
- V : State_Val)
- is
- Value : constant String := State_Val'Image (V);
- begin
- S (Index * 11 + 1 .. Index * 11 + Value'Length) := Value;
- end Insert_Image;
-
- -------------------
- -- Extract_Value --
- -------------------
-
- function Extract_Value (S : String; Index : Integer) return State_Val is
- Start : constant Integer := S'First + Index * Image_Numeral_Length;
- begin
- return State_Val'Value (S (Start .. Start + Image_Numeral_Length - 1));
- end Extract_Value;
-
-end System.Random_Numbers;